Modeling n-furcated liver vessels from a 3-D segmented volume using hole-making and subdivision methods.

It is difficult to build an accurate and smooth liver vessel model due to the tiny size, noise, and n-furcations of vessels. To overcome these problems, we propose an n-furcation vessel tree modeling method. In this method, given a segmented volume and a point indicating the root of the vessels, centerlines and cross-sectional contours of the vessels are extracted and organized as a tree first. Then, the tree is broken up into separate branches in descending order of length, and polygonal meshes of all the branches are separately constructed from the cross-sectional contours. Finally, all the meshes are combined sequentially using our hole-making approach. Holes are made on a coarse mesh, and a final fine mesh is generated using a subdivision method. The hole-making approach with the subdivision method provides good efficiency in mesh construction as well as great flexibilities in mesh editing. Experiments show that our method can automatically construct smooth mesh models for n-furcated vessels with mean absolute error of 0.92 voxel and mean relative error of 0.17. It is promising to be used in diagnosis, analysis, and surgery simulation of liver diseases, and is able to model tubular structures with tree topology.